Example:An automobile manufacturer provides vehicles equipped with selected options. Each vehicle is ordered;- with or without an automatic transmission,- with or without air conditioning- with one of three choices of a stereo system- with one of four exterior colors

BONUS:

Consider the automobile manufacturer includes interior color as another option. There are four choices of interior color; red, black, blue or brown.However;- with a red exterior, only a black or red interior can be chosen- with a white exterior, any interior color can be chosen,- with a blue exterior, only a black, red or blue interior can be chosen- with a brown exterior, only a brown interior can be chosen.

Q: Use tree diagram to determine # sample points

• Example: Consider a recent study conducted by the personnel manager of

a major computer software company. The study showed that 30% of employees who left the firm

within two years did so primarily because they were dissatisfied with their salary, 20% left because they were dissatisfied with their work assignments, 12% of the former employees indicated dissatisfaction with both their salary and their work assignments.

• Question:What is the probability that an employee who leaves within two

years does so because of dissatisfaction with salary, dissatisfaction with work assignment or both?

Assigning ProbabilitiesAssigning Probabilities

Basic Requirements for Assigning ProbabilitiesBasic Requirements for Assigning Probabilities

2. The sum of the probabilities for all experimental2. The sum of the probabilities for all experimental outcomes must equal 1.outcomes must equal 1. 2. The sum of the probabilities for all experimental2. The sum of the probabilities for all experimental outcomes must equal 1.outcomes must equal 1.

PP((EE11) + ) + PP((EE22) + . . . + ) + . . . + PP((EEnn) = 1) = 1

where:where:nn is the number of experimental outcomes is the number of experimental outcomes

Multiplication LawMultiplication Law

The The multiplication lawmultiplication law provides a way to compute the provides a way to compute the probability of the intersection of two events.probability of the intersection of two events. The The multiplication lawmultiplication law provides a way to compute the provides a way to compute the probability of the intersection of two events.probability of the intersection of two events.

The law is written as:The law is written as: The law is written as:The law is written as:

PP((AA BB) = ) = PP((BB))PP((AA||BB))PP((AA BB) = ) = PP((BB))PP((AA||BB))

Do not confuse the notion of mutually exclusiveDo not confuse the notion of mutually exclusive events with that of independent events.events with that of independent events. Do not confuse the notion of mutually exclusiveDo not confuse the notion of mutually exclusive events with that of independent events.events with that of independent events.

Two events with nonzero probabilities cannot beTwo events with nonzero probabilities cannot be both mutually exclusive and independent.both mutually exclusive and independent. Two events with nonzero probabilities cannot beTwo events with nonzero probabilities cannot be both mutually exclusive and independent.both mutually exclusive and independent.

If one mutually exclusive event is known to occur,If one mutually exclusive event is known to occur, the other cannot occur.; thus, the probability of thethe other cannot occur.; thus, the probability of the other event occurring is reduced to zero (and theyother event occurring is reduced to zero (and they are therefore dependent).are therefore dependent).

If one mutually exclusive event is known to occur,If one mutually exclusive event is known to occur, the other cannot occur.; thus, the probability of thethe other cannot occur.; thus, the probability of the other event occurring is reduced to zero (and theyother event occurring is reduced to zero (and they are therefore dependent).are therefore dependent).

Mutual Exclusiveness and IndependenceMutual Exclusiveness and Independence

Two events that are not mutually exclusive, mightTwo events that are not mutually exclusive, might or might not be independent.or might not be independent. Two events that are not mutually exclusive, mightTwo events that are not mutually exclusive, might or might not be independent.or might not be independent.

Example-1: An insurance company sells a 10,000 TRL 1-year term insurance policy at an annual premium of 290 TRL. Based on many year’s information, the probability of death during the next year for a person of customer’s age, sex, health etc. is 0.001Q: What is the expected gain (amount of money made by the company) for a policy of this type?